The field of invention is analog electrical circuits, more particularly, this invention relates to operational amplifiers with increased gain in a wide bandwidth.
An operational amplifier, hereinafter referred to as an xe2x80x9copamp,xe2x80x9d is a general building block used in numerous analog electrical circuits. The symbol used to represent a general-purpose opamp [32] is shown in FIG. 1. A differential-input single-ended-output opamp [32] has a non-inverting input terminal [34], an inverting input terminal [36], and an output terminal [38], the voltage Vout of which is defined with respect to a ground terminal [40]. In the ideal case, the two input terminals [34] and [36] are high-impedance terminals, i.e., they do not conduct any current, and the output voltage Vout is a factor of A higher than the differential input voltage Vin, where the gain A approaches infinity. In principle, the output voltage Vout will depend only on the voltage difference Vin between the two input terminals [34] and [36], not on their average voltage with respect to the ground terminal [40], i.e., the common-mode input voltage. Hence, for an ideal infinite-gain opamp the ground terminal""s [40] potential is somewhat arbitrary.
Opamps are generally used in feedback configurations. FIG. 2 shows a typical feedback configuration which may be used, for example, for current-to-voltage conversion in combination with a current-mode digital-to-analog converter. The reference potential for the output voltage Vout is obtained by connecting the non-inverting input terminal [34] to the ground terminal [40]. If the opamp""s [32] gain A is indeed infinite and the system is stable, the inverting input terminal [36] will have the same potential as the ground terminal [40]. A linear impedance element [42] is connected between the inverting input terminal [36] and the output terminal [38]. The impedance element[42] is a one-port network, usually consisting of only resistors, capacitors, and possibly also inductors, which here is described by the Laplace-transformed impedance Z(s). Hence, the output voltage is described by the Laplace-transformed relationship
Vout(s)=Z(s)xc2x7Iin(s).xe2x80x83xe2x80x83(1)
Physical opamps are not ideal. The gain A is not infinite, and variations in the output voltage Vout are delayed with respect to variations in the input voltage Vin. For small signals the opamp can be characterized by a transfer function,
Vout(s)=Hopamp(s)xc2x7Vin(s).xe2x80x83xe2x80x83(2)
The opamp""s [32] gain A(f) is frequency-dependent, typically with a high static value Adc=Hopamp(0). When taking Equation 2 into account, Equation 1 takes the form                                           V            out                    ⁡                      (            s            )                          =                                                            Z                ⁡                                  (                  s                  )                                            ·                                                I                  in                                ⁡                                  (                  s                  )                                                      -                                          V                in                            ⁡                              (                s                )                                              =                                                                      Z                  ⁡                                      (                    s                    )                                                  ·                                                      I                    in                                    ⁡                                      (                    s                    )                                                                              1                +                                  1                  /                                                            H                      opamp                                        ⁡                                          (                      s                      )                                                                                            .                                              (        3        )            
One of the difficulties in using non-ideal opamps is that the closed-loop system, e.g. the circuit shown in FIG. 2, may become unstable if the system""s open-loop frequency response HOL(s) is not properly designed. The open-loop frequency response HOL(s) is the product of the opamp""s frequency response Hopamp(s) and the feedback network""s frequency response xcex2(s). The feedback network""s frequency response xcex2(s) can be evaluated as       β    ⁢          (      s      )        =            -                        V          in                ⁢                  (          s          )                                    V        out            ⁢              (        s        )            
when the opamp is removed from the circuit, provided that its input/output impedances are properly modeled. The accurate calculation of the open-loop frequency response HOL(s) requires some experience, but it is discussed in several textbooks and taught at most electrical engineering schools; hence the concept is well-known to those ordinarily skilled in the art. For the closed-loop circuit shown in FIG. 2, the feedback network""s frequency response is xcex2(s)=1, and thus, HOL(s)=Hopamp(s).
Stability/instability can be determined using one of several stability criterions. Nyquist""s stability criterion will be used for the following discussion. Nyquist""s stability criterion states that the closed-loop system will be stable if the polar plot of HOL (s), s=j2xcfx80f, f∈R, does not encircle the point xe2x88x921, otherwise the system will be unstable. For all real systems, HOL(j2xcfx80f) and HOL(xe2x88x92j2xcfx80f) are complex-conjugate values, hence it is sufficient to plot HOL(j2xcfx80f) for positive values of f only (and connect HOL(0) and limfxe2x86x92∞HOL(j2xcfx80f) by a straight line).
It is unavoidable that stray capacitors will make the angle xcfx86(f) of an opamp""s frequency response Hopamp(j2xcfx80f)=A(f)xc2x7ejxc2x7xcfx86(f), i.e., the phase response, uncontrollable at high frequencies, which is why it is necessary to reduce the gain A(f) to less than 1 at such high frequencies. Opamps are usually designed to have a frequency response similar to that shown in FIGS. 3, 4, and 5. FIG. 3 shows the opamp""s gain A in deci Bell (dB) versus the frequency f in Hertz on a logarithmic scale. The opamp""s unit-gain frequency, which is also called the opamp""s gain-bandwidth frequency fgbw, is an important parameter. The typical target opamp-gain characteristic is A(f)=fgbw/f=xe2x88x9220xc2x7log10(f/fgbw) dB, but the gain is generally limited at low frequencies. In other words, the opamp""s frequency response has a pole at a low frequency fpole,1. Although the low-frequency (dominating) pole fpole,1 is intentional, the parameters fpole,1 and Adc are usually somewhat undetermined; an opamp should be designed to have a well-controlled fgbw, which is the most important parameter with respect to stability concerns.
FIG. 4 shows a plot of the phase response xcfx86(f) in degrees versus the frequency f. The phase margin is defined as 180xc2x0+xcfx86(fgbw). A general design rule is to make the phase margin at least 45xc2x0. This will generally require that fgbw is slightly lower that the opamp""s first non-dominating non-canceled (undesired) pole/right-plane-zero. The achievable fgbw is dependent on the technology used and the power consumption allowed.
FIG. 5 shows a polar plot of the frequency response Hopamp(j2xcfx80f); it is merely an alternative graphical representation of A(f) and xcfx86(f). The respective closed-loop system, i.e., the circuit shown in FIG. 2, is stable because the curve does not encircle the critical point xe2x88x921. Clearly, a large phase margin is preferable because that will avoid close proximity of the critical point and the area enclosed by Hopamp(j2xcfx80f), f∈R (which is the main stability concern).
FIG. 6 shows the conceptual topology of a simple one-stage opamp (often also called an OTA). The opamp consists of only one transconductance stage [44] providing an output current Iout proportional to the differential input voltage Vin,
Iout(s)=gmxc2x7Vin(s).xe2x80x83xe2x80x83(4)
Equation 4 is valid for frequencies up to a certain frequency fxe2x80x2 only. Hence the gain of the opamp must be less than one at frequencies higher than fxe2x80x2. The opamp""s voltage gain A(f) is determined by the load [46], which is modeled as a resistor [48] Rload and a capacitor [50] Cload connected in parallel. The opamp""s static gain is
Adc=gmxc2x7Rload xe2x80x83xe2x80x83(5)
and its unity-gain frequency is                               f          gbw                =                                            g              m                                      2              ⁢              π              ⁢                              xe2x80x83                            ⁢                              C                load                                              .                                    (        6        )            
Because the transconductance gm cannot be made arbitrarily high (for a limited power/current consumption), this type of opamp provides only relatively little static gain when driving a resistive load [48]. Because the unity-gain frequency (and thus the circuit""s speed/stability) depends on the capacitive load [50], this opamp type is best suited for applications driving only on-chip capacitive loads; it is used frequently for the implementation of switched-capacitor circuits.
Multi-stage opamps are better suited to drive difficult loads, such as low-ohmic resistive loads, long cables, loudspeakers, etc. FIG. 7 shows the conceptual topology of a two-stage opamp [52]. The first stage is a differential-input transconductance stage [54]. This stage [54] is cascaded with an inverting amplifier [56] which should be powerful enough to drive the RC load [46] while providing gain A0 greater than (say) 3 for frequencies lower than fgbw. A compensation capacitor [58] Cint provides negative feedback for the second stage [56], whereby the opamp""s [52] frequency response will be approximately                                           H            opamp                    ⁡                      (            s            )                          =                                            g              m                                      s              ⁢                              xe2x80x83                            ⁢                              C                int                                              .                                    (        7        )            
Because Cint is usually an on-chip capacitor, the system""s speed/stability is relatively well-controlled and independent of the capacitive load Cload. The opamp""s [52] static gain is the product of the static gain of the first stage [54] and the static gain of the second stage [56]. The static gain of the first stage [54] is the product of the transconductance gm1 and the static impedance (ohmic load) of the node connecting the two stages [54] [56]. Dependent on the actual implementation, the first stage""s [54] gain can be anywhere in the range from (say) 30 dB to 100 dB. The static gain of the second stage [56] is usually relatively smaller, say 30 dB.
When the supply voltage is relatively low, the output stage of a multi-stage opamp is often merely a transconductance stage, as opposed to a voltage amplifier with a low output impedance. FIG. 8 shows the topology of a typical two-stage opamp with a transconductance output stage [62]. When the static gain gm,2xc2x7Rload of the output stage [62] is relatively high, the higher output impedance does not pose a problem. However, when the resistive load [48] is low-ohmic, gm,2xc2x7Rload may be quite low, possibly less than one. In that case the opamp""s [60] gain is generated almost entirely in the first stage [60].
U.S. Pat. No. 4,559,502 (December 1985) to Huijsing et al. describes a multi-stage opamp with more than two stages, suitable for driving low-ohmic loads. A frequency response similar to that shown in FIGS. 3, 4, and 5 is obtained by using a so-called nested-miller compensation technique. In a nested-miller compensated opamp, multiple compensation capacitors are connected from the output node to intermediate nodes in-between the individual stages, see FIG. 9. The advantage of this technique is that a very high static gain can be obtained using only low-gain stages, but the overall unity-gain frequency and especially the slew-rate/power performance is degraded. The lower unity-gain frequency is caused by what is known as the right-plane-zero problem, i.e., the opamp""s polarity is changed when the compensation capacitors, C2, C3, and C4, short-circuit the respective transconductance stages, gm,2, gm,3, and gm,4, a high frequencies. A variation of this technique, shown in FIG. 10, which overcomes this problem is discussed in U.S. Pat. No. 5,155,447 (October 1992), also to Huijsing et al., and by Fan You et al. (Multistage Amplifier Topologies with Nested Gm-C Compensation, IEEE Journal of Solid-State Circuits, Vol. 32, No. 12, 1997). U.S. Pat. No. 5,485,121 (January 1996) to Huijsing et al. and U.S. Pat. No. 5,854,573 (December 1998) to Chan are based on the same technique to avoid the change of polarity at high frequencies. U.S. Pat. No. 5,486,790 (January 1996) to Huijsing et al. discusses a hybrid-nested-miller compensation technique, whereby the capacitive load of the output terminal is reduced, thus improving the slew-rate/power ratio.
Gain and bandwidth parameters do not describe an opanip""s performance in full detail. Both these parameters are based on the assumption that the opamp is a linear device, which is only rarely the case. In fact, if opamps were linear the gain response A(f) would often be of only secondary interest. However, opamps are generally quite nonlinear. The output stage is particularly nonlinear because it will exhibit a large voltage swing, and especially if it has to provide a large current to the load. However, provided the opamp has xe2x80x9cinfinitexe2x80x9d gain, and that it is used in a negative-feedback configuration, e.g., as shown in FIG. 2, the external linearity will depend only on the feedback network""s linearity. It is well-known that errors which occur in an opamp""s output stage will be suppressed (when they are referred to the output) by the gain of the open-loop frequency response HOL(s)=xcex2(s)xc2x7Hopamp(s). Thus, if the opamp is designed to have the frequency response shown in FIGS. 3, 4, and 5, the external linearity will deteriorate as the signal frequency is increased relative to the opamp""s unity-gain frequency. Asynchronous digital subscriber line (ADSL) modems, for example, have a signal bandwidth of several mega Hertz, and they require that the driver interfacing a long cable has a linearity of at least 80-90 dB. This is very hard to achieve. Using standard design techniques, this level of performance will require that the opamp per se is relatively linear, and that it has a very high unity-gain frequency, say in the giga-Hertz range. Considering that the capacitive load generally is quite large, it will be understood that drivers for ADSL modems are a very challenging design problem.
Another significant problem inherent to most opamps is that errors caused by the first stage are not suppressed at all. Slew-rate limitation is a well-know example of this problem. Consider the two-stage opamp shown in FIG. 7. The voltage swing of the internal node connecting the two stages [54] and [56] is generally relatively small. Thus, when the output voltage changes, approximately the same voltage variation will occur across the compensation capacitor [58], and the input stage [54] must provide the required charge. The current that needs to be provided by the input stage [54] is proportional to the signal frequency and the magnitude of the opamp""s [52] output voltage. Considering that the first stage""s [54] linearity is generally a decreasing function of the magnitude of the current provided, it can be concluded that the linearity (once again) will deteriorate as the signal frequency is increased. In the extreme case, the input stage [54] will saturate, which results in slew-rate distortion. Clearly, the multi-stage structures shown in FIGS. 9 and 10 do not ease the requirements to the input stage because the voltage across the compensation capacitors will vary synchronously with the output voltage, thus requiring all the transconductance stages to provide current signals proportional to the signal frequency and magnitude.
A fundamental difficulty of designing opamps is that the optimization of the input stage""s linearity, the minimization of the opamp""s noise and power consumption, and the maximization of the unity-gain frequency are conflicting requirements. Consider, for example, the implementation of the two-stage amplifier shown in FIG. 11. The first transconductance stage [66] provides a differential output, for which the non-inverting output is used to implement a feedforward path [68] connected directly to the overall output [70]. The advantage of this technique is discussed by Huijsing in U.S. Pat. No. 5,485,121. Consider the design of the differential pair [72] generating the first stage""s [66] transconductance gm,1. A high transconductance gm,1 is preferable to minimize the input-referred noise and to maximize the unity-gain frequency. The transconductance can be maximized by increasing the differential pair""s [72] aspect ratio, but that will decrease the input stage""s [66] linear range. The linearity can be improved by increasing the differential pair""s [72] effective overdrive, or by inserting degenerative resistors (not shown) in series with the source terminals; both of which will deteriorate the opamp""s power/speed ratio.
The conclusion is that it is difficult to achieve good external linearity at high signal frequencies. If the internal linearity is emphasized, the unity-gain frequency will be relatively lower and there will be less gain available to improve the linearity. On the other hand, if the unity-gain frequency, and thus the gain, is emphasized the linearity will be poor and relatively more gain needed to achieve the required level of external linearity.
A linear wide-bandwidth negative-feedback system according to this invention comprises a high-speed driver and a slower linear controller selectively suppressing the error signal in the system""s signal band.
Accordingly, several objects and advantages of the present invention are
to provide an operational amplifier circuit which can be used to drive difficult loads, such as for ASDL modems, and provide good external linearity in a wide bandwidth;
to provide an operational amplifier circuit for which the unity-gain frequency and the linearity can be optimized independently and simultaneously;
to provide a method for the design of stable closed-loop circuits based on operational amplifiers, for which the opamp gain A(f) can be vastly higher than fgbw/f for signal-band frequencies up to approximately {fraction (1/10)} of the unity-gain frequency fgbw;
to provide an operational amplifier circuit for which errors caused by slew-rate limitation will be efficiently suppressed;
to provide a buffer circuit based on an open-loop feed-forward path and an operational amplifier, such that the feed-forward path""s distortion is suppressed by the opamp""s gain, and such that the opamp can be implemented with a relatively smaller output stage and, thus, with a relatively higher unity-gain frequency.
Further objects and advantages will become apparent from a consideration of the ensuing description, the drawings, and the claims.